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3In this work, Valanis model parameters, and their variation with bolt preload, were determined for a bolted lap 4 joint, which consisted in two steel plates held together by a metric 12 screw. For this purpose, a series of transitory non-5 linear analyses were performed on the basis of a three dimensional finite element model of the bolted lap joint subjected to 6 varying bolt preloads and tangential displacements. Curve fitting of hysteresis cycles obtained from numerical simulations 7 allowed determination of Valanis model parameters as well as assessment of bolt preload influence on these parameters. In 8 addition, the present numerical simulations provided information about the evolution of the contact state from stick to slip 9 regimes between the bolted plates, reflecting the non-linear behaviour of the joint. Quasi-static tests at several preloads and 10 tangential displacements conditions were conducted to validate Valanis model parameters previously obtained from 11 numerical simulations. The present findings provided detailed information about the evolution of the aforementioned 12 Valanis parameters with bolt preload. Thus, we confirmed that equivalent stiffness values corresponding to the macro-slip 13 regime as well as the upper limit of the sticking regime (E t , and  0 , respectively) are highly influenced by bolt preload 14 levels. These results may prove useful to appropriately design bolted joints to be used under specific stiffness and damping 15 criteria, and therefore reducing the vibration response of the joint. 16 17 18

Author Comments:The authors after the review have prepared all the images to be published in black and white. Fig1 has been generated using PPT, fig 2 is a photo, fig 3 to 11 have been generated using excel and they have been introduced in a word or a power point.All the tables are generated using word.Response to Reviewers: Dear reviewers and editor,We appreciate your consideration and your comments to improve the quality of the paper that we have tried to follow. We send also the manuscript with the modifications highlighted as a suplementary file-Yours faithfully,